In multi-objective optimization, a standard approach to optimizing OWAs is to solve the equivalent linear program derived by [1]}. Because the utilities depend on 3d-tensors \(P\in \mathcal {P}\)  in our case, the linear program has \(O(n \cdot m^2)\)  variables and constraints, which is prohibitively large in practice.
Another approach consists in using online subgradient descent to optimize GGFs, like [2]}, [3]}.
This is not tractable in our case because it requires to project iterates onto the parameter space, which in our case involves costly projections onto the space of ranking policies \(\mathcal {P}.\) 
On the other hand, the Frank-Wolfe algorithm [4]} was shown to provide a computationally efficient and provably convergent method to optimize over \(\mathcal {P}\)  [5]}. However, it only applies to smooth functions, and
Frank-Wolfe with subgradients may not converge to an optimal solution [6]}.
